Background: Reduction or elimination of by-product formation is of immediate economic relevance in fermentation processes for industrial bioethanol production with the yeast Saccharomyces cerevisiae. Anaerobic cultures of wild-type S. cerevisiae require formation of glycerol to maintain the intracellular NADH/NAD⁺ balance. Previously, functional expression of the Calvin-cycle enzymes ribulose-1,5-bisphosphate carboxylase (RuBisCO) and phosphoribulokinase (PRK) in S. cerevisiae was shown to enable reoxidation of NADH with CO₂ as electron acceptor. In slow-growing cultures, this engineering strategy strongly decreased the glycerol yield, while increasing the ethanol yield on sugar. The present study explores engineering strategies to improve rates of growth and alcoholic fermentation in yeast strains that functionally express RuBisCO and PRK, while maximizing the positive impact on the ethanol yield. Results: Multi-copy integration of a bacterial-RuBisCO expression cassette was combined with expression of the Escherichia coli GroEL/GroES chaperones and expression of PRK from the anaerobically inducible DAN1 promoter. In anaerobic, glucose-grown bioreactor batch cultures, the resulting S. cerevisiae strain showed a 31% lower glycerol yield and a 31% lower specific growth rate than a non-engineered reference strain. Growth of the engineered strain in anaerobic, glucose-limited chemostat cultures revealed a negative correlation between its specific growth rate and the contribution of the Calvin-cycle enzymes to redox homeostasis. Additional deletion of GPD2, which encodes an isoenzyme of NAD⁺-dependent glycerol-3-phosphate dehydrogenase, combined with overexpression of the structural genes for enzymes of the non-oxidative pentose-phosphate pathway, yielded a CO₂-reducing strain that grew at the same rate as a non-engineered reference strain in anaerobic bioreactor batch cultures, while exhibiting a 86% lower glycerol yield and a 15% higher ethanol yield. Conclusions: The metabolic engineering strategy presented here enables an almost complete elimination of glycerol production in anaerobic, glucose-grown batch cultures of S. cerevisiae, with an associated increase in ethanol yield, while retaining near wild-type growth rates and a capacity for glycerol formation under osmotic stress. Using current genome-editing techniques, the required genetic modifications can be introduced in one or a few transformations. Evaluation of this concept in industrial strains and conditions is therefore a realistic next step towards its implementation for improving the efficiency of first- and second-generation bioethanol production.